In my opinion, the most important conclusion of this paper is that occasional but widespread hybridization among bears is why it has been so hard to say with confidence when polar bears arose (which I addressed years ago, in my Polar bear evolution series: Part 1, Part 2, and Part 3). You cannot use traditional methods of pinpointing the timing of speciation events from genetic data if one or more of the species have hybridized (traded genes). See the long, fuzzy “divergence times” for bears in the image below from the Kumar paper.

From Kumar et al. 2017, Fig. 5: “The scale bar shows divergence times in million years and 95% confidence intervals for divergence times [speciation events] are shown as shadings.”

From the Kumar et al. 2017 abstract (my bold):

“Strong ancestral gene flow between the Asiatic black bear and the ancestor to polar, brown and American black bear explains uncertainties in reconstructing the bear phylogeny. Gene flow across the bear clade may be mediated by intermediate species such as the geographically wide-spread brown bears leading to large amounts of phylogenetic conflict.

…

Evidence for extensive inter-specific gene flow, found also in other animal species, necessitates shifting the attention from speciation processes achieving genome-wide reproductive isolation to the selective processes that maintain species divergence in the face of gene flow.”

In other words, a species of bear (or any other organism) is the totality of the physical form, behaviour, physiology, and life history traits that make it a unique entity.

A few instances of hybridization that produce fertile offspring does not negate the unique species status of any animal (see discussion here).

All of the species of bears tested by Kumar and colleagues (see their Figure 4 below) are unique entities and true species.